Question

A manufacturer claims that lifespans for their coffee machines (in months) can be described by a normal distribution with a mean of 54 and a standard deviation of 6.5. About 10.03% of their coffee machines last longer than how many months?

A) 60.73 months
B) 47.27 months
C) 70.85 months
D) 65.96 months

Answer 1

To find the number of months that the coffee machines last longer than given probability, we can use the normal distribution and z-scores. Option B) 47.27 months is the correct answer.

Step-by-step explanation:

To answer this question, we can use the concept of z-scores. First, we need to find the z-score for the given probability. Since the normal distribution is symmetric, we can find the z-score that corresponds to the 10.03% probability on one side of the distribution. Using a standard normal distribution table or a calculator, we find that the z-score is approximately -1.28.

Next, we can use the z-score formula to find the corresponding value in terms of months:

x = mean + (z * standard deviation)

Substituting the values, we get:

x = 54 + (-1.28 * 6.5)

Simplifying the calculation, the value of x is approximately 46.27 months. Therefore, option B) 47.27 months is the correct answer.